few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Prove theorems involving similarity.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Explain volume formulas and use them to solve problems.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand and apply theorems about circles.

Translate between the geometric description and the equation for a conic section.

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Visualize relationships between two-dimensional and three-dimensional objects.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand similarity in terms of similarity transformations.

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Prove geometric theorems.

Make geometric constructions.

Solve real-world and mathematical problems involving area, surface area, and volume.

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Classify two-dimensional figures into categories based on their properties.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Reason with shapes and their attributes.

Analyze, compare, create, and compose shapes.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Find arc lengths and areas of sectors of circles.
problem_activity: Problem 1
In the diagram below,
$${m\parallel p}$$
.
[IMG]
a. Write three equations that are perpendicular to line
$$m$$
.
b. What is the relationship between your three equations and line
$$p$$
?
c. Find the distance between line
$$m$$
and
$$p$$
using your three equations. What do you notice?
Problem 2
In the diagram below,
$${\overleftrightarrow {AI} \parallel {\overleftrightarrow {CK}}}$$
and
$${\overleftrightarrow{IC} \perp \overleftrightarrow {AK}}$$
. How can you use the triangles
$${AHI}$$
and
$${KHC}$$
to prove that the slopes for
$${\overleftrightarrow{AI}}$$
and
$${\overleftrightarrow {CK}}$$
are the same?
[IMG]
Problem 3
Write three equations that are parellel to
$${\overleftrightarrow{AB}}$$
.
[IMG]


correct_option_index: 8